{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Sampling and Distributions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true,
    "hide": true
   },
   "outputs": [],
   "source": [
    "# The %... is an iPython thing, and is not part of the Python language.\n",
    "# In this case we're just telling the plotting library to draw things on\n",
    "# the notebook, instead of on a separate window.\n",
    "%matplotlib inline\n",
    "# See all the \"as ...\" contructs? They're just aliasing the package names.\n",
    "# That way we can call methods like plt.plot() instead of matplotlib.pyplot.plot().\n",
    "import numpy as np\n",
    "import scipy as sp\n",
    "import matplotlib as mpl\n",
    "import matplotlib.cm as cm\n",
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd\n",
    "import time\n",
    "pd.set_option('display.width', 500)\n",
    "pd.set_option('display.max_columns', 100)\n",
    "pd.set_option('display.notebook_repr_html', True)\n",
    "import seaborn as sns\n",
    "sns.set_style(\"whitegrid\")\n",
    "sns.set_context(\"poster\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Expectations and Variance\n",
    "\n",
    "The **expectation value** of a quantity with respect to the a distribution is the weighted sum of the quantity where the weights are probabilties from the distribution. For example, for the random variable $X$:\n",
    "\n",
    "$$E_p[X] = \\sum_x x\\,p(x).$$\n",
    "\n",
    "$E_p[X]$ if often just called the expectation value of the distribution. This definition is analogous to the one for the arithmetic mean of a dataset: the only difference is that we want to give more weight to more probable values.\n",
    "\n",
    "The variance of a distribution is defined analogous to that of a dataset:\n",
    "\n",
    "$$V_p[X] = E_p[(X-E_p[X])^2]$$.\n",
    "\n",
    "For the Bernoulli distribution $p(x)=p=constant$, and you are summing it over ones as opposed to 0's, so the mean is just p. The variance is $(1-p)^2\\times p +(-p)^2\\times (1-p) = p(1-p)(1-p+p) = p(1-p)$.\n",
    "\n",
    "In general, we can find this mean that by obtaining a large bunch of samples from the distribution and find their arithmetic mean. The justification for this is the Law of large numbers, which we'll come to soon. \n",
    "\n",
    "However the intuition is obvious: for a large number of samples, the frequencies will tract probabilities well, so high probability samples with roughly the same value will re-occur, and a simple arithmetic sun will capture the curves of the distribution."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### The Law of Large Numbers\n",
    "\n",
    "Lets keep increasing the length of the sequence of coin flips n, and compute a running average $S_n$ of the coin-flip random variables,\n",
    "$$S_n = \\frac{1}{n} \\sum_{i=1}^{n} x_i .$$\n",
    "We plot this running mean, and notice that it converges to the mean of the distribution from which the random variables are plucked, ie the Bernoulli distribution with p=0.5. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from scipy.stats.distributions import bernoulli\n",
    "def throw_a_coin(n):\n",
    "    brv = bernoulli(0.5)\n",
    "    return brv.rvs(size=n)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "random_flips = throw_a_coin(10000)\n",
    "running_means = np.zeros(10000)\n",
    "sequence_lengths = np.arange(1,10001,1)\n",
    "for i in sequence_lengths:\n",
    "    running_means[i-1] = np.mean(random_flips[:i])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false,
    "figure_caption": "The Law of Large Numbers: means of sequences converge to the distribution mean.",
    "figure_type": "m"
   },
   "outputs": [
    {
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oCTubn0gCbUkzJdGWFAAAwIxQYFJWlC2nI/AroS3puOdeqQtdvuaiKgtXMnfB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\nERERkYdjUEBERERE5OH+P2TFkSVr30XuAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10aa8dd10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(sequence_lengths, running_means);\n",
    "plt.xscale('log')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "This is an example of a very important theorem in statistics, the law of large numbers, which says this:\n",
    "\n",
    "**Let $x_1,x_2,...,x_n$ be a sequence of independent, identically-distributed (IID) random variables. Suppose that $X$ has the finite mean $\\mu$. Then the average of the first n of them:**\n",
    "\n",
    "$$S_n = \\frac{1}{n} \\sum_{i=1}^{n} x_i ,$$\n",
    "\n",
    "**converges to the mean of the variables $\\mu$ as $n \\to \\infty$:**\n",
    "\n",
    "$$ S_n \\to \\mu \\, as \\, n \\to \\infty. $$\n",
    "\n",
    "The law of large numbers is what makes the **frequentist** interpretation of probability possible. For consider any event $E$ from a probability distribution with random variable Y, and consider the indicator function $I_E$ such that:\n",
    "\n",
    "\\begin{eqnarray*}\n",
    "I_E(y) = 1 \\,&& if \\, y \\in E\\\\\n",
    "I_E(y) = 0 \\,&&  otherwise\n",
    "\\end{eqnarray*}\n",
    "\n",
    "The variable $Z=I_E(Y)$ is now Bernoulli random variable with parameter and thus p = P(E). Now if we take a long sequence from $Y$ and thus $Z$, then the frequency of successes (where success means being in E) will converge by the law of large numbers to the true probability p."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Having now established something about long sequences of random variables, lets turn to samples from the population of random numbers.\n",
    "\n",
    "### Samples from a population of coin flips\n",
    "\n",
    "Lets redo the experiment with coin flips that we started in the previous lab. We'll establish some terminology at first. What we did there was to do a large set of replications M, in each of which we did many coin flips N.  We'll call the result of each coin flip an observation, and a single replication a sample of observations. Thus the number of samples is M, and the sample size is N. These samples have been chosen from a population of size $n >> N$.\n",
    "\n",
    "We show the mean over the observations, or sample mean, for a sample size of 10, with 20 replications. There are thus 20 means."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def make_throws(number_of_samples, sample_size):\n",
    "    start=np.zeros((number_of_samples, sample_size), dtype=int)\n",
    "    for i in range(number_of_samples):\n",
    "        start[i,:]=throw_a_coin(sample_size)\n",
    "    return np.mean(start, axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.6,  0.5,  0.6,  0.7,  0.4,  0.3,  0.6,  0.6,  0.5,  0.5,  0.3,\n",
       "        0.5,  0.4,  0.8,  0.6,  0.5,  0.4,  0.5,  0.7,  0.4])"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "make_throws(number_of_samples=20, sample_size=10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us now do 200 replications, each of which has a sample size of 1000 flips, and store the 200 means for each sample zise from 1 to 1000 in `sample_means`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "sample_sizes=np.arange(1,1001,1)\n",
    "sample_means = [make_throws(number_of_samples=200, sample_size=i) for i in sample_sizes]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Lets formalize what we are up to. Lets call the N random variables in the $m^{th}$ sample $x_{m1},x_{m2},...,x_{mN}$ and lets define the sample mean\n",
    "\n",
    "$$\\bar{x_m}(N) = \\frac{1}{N}\\, \\sum_{i=1}^{N} x_{mi} $$\n",
    "\n",
    "Now imagine the size of the sample becoming large, asymptoting to the size of an infinite or very large population (ie the sample becomes the population). Then you would expect the sample mean to approach the mean of the population distribution. This is just a restatement of the law of large numbers.\n",
    "\n",
    "Of course, if you drew many different samples of a size N (which is not infinite), the sample means $\\bar{x_1}$, $\\bar{x_2}$, etc would all be a bit different from each other. But the law of large numbers intuitively indicates that as the sample size gets very large and becomes an infinite population size, these slightly differeing means would all come together and converge to the population (or distribution) mean.\n",
    "\n",
    "To see this lets define, instead, the mean or expectation of the sample means over the set of samples or replications, at a sample size N:\n",
    "\n",
    "$$E_{\\{R\\}}(\\bar{x}) = \\frac{1}{M} \\,\\sum_{m=1}^{M} \\bar{x_m}(N) ,$$\n",
    "where $\\{R\\}$ is the set of M replications, and calculate and plot this quantity."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "mean_of_sample_means = [np.mean(means) for means in sample_means]\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false,
    "figure_caption": "The mean of sample means also approaches the distribution mean.",
    "figure_type": "m"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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REREll4OCDUYbRERERETJ5JhgIxxO9REQERERETmLY4INZjaIiIiIiJLLMcEGO4gTERER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\nTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10921da10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(sample_sizes, mean_of_sample_means);\n",
    "plt.ylim([0.480,0.520]);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Not surprisingly, the mean of the sample means converges to the distribution mean as the sample size N gets very large.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### The notion of a Sampling Distribution\n",
    "\n",
    "In data science, we are always interested in understanding the world from incomplete data, in other words from a sample or a few samples of a population at large. Our experience with the world tells us that even if we are able to repeat an experiment or process, we will get more or less different answers the next time. If all of the answers were very different each time, we would never be able to make any predictions.\n",
    "\n",
    "But some kind of answers differ only a little, especially as we get to larger sample sizes. So the important question then becomes one of the distribution of these quantities from sample to sample, also known as a **sampling distribution**. \n",
    "\n",
    "Since, in the real world, we see only one sample, this distribution helps us do **inference**, or figure the uncertainty of the estimates of quantities we are interested in. If we can somehow cook up samples just somewhat different from the one we were given, we can calculate quantities of interest, such as the mean on each one of these samples. By seeing how these means vary from one sample to the other, we can say how typical the mean in the sample we were given is, and whats the uncertainty range of this quantity. This is why the mean of the sample means is an interesting quantity; it characterizes the **sampling distribution of the mean**, or the distribution of sample means.\n",
    "\n",
    "We can see this mathematically by writing the mean or expectation value of the sample means thus:\n",
    "\n",
    "$$E_{\\{R\\}}(N\\,\\bar{x}) = E_{\\{R\\}}(x_1 + x_2 + ... + x_N) = E_{\\{R\\}}(x_1) + E_{\\{R\\}}(x_2) + ... + E_{\\{R\\}}(x_N)$$\n",
    "\n",
    "Now in the limit of a very large number of replications, each of the expectations in the right hand side can be replaced by the population mean using the law of large numbers! Thus:\n",
    "\n",
    "\\begin{eqnarray*}\n",
    "E_{\\{R\\}}(N\\,\\bar{x}) &=& N\\, \\mu\\\\\n",
    "E(\\bar{x}) &=& \\mu\n",
    "\\end{eqnarray*}\n",
    "\n",
    "which tells us that in the limit of a large number of replications the expectation value of the sampling means converges to the population mean. This limit gives us the true sampling distribution, as opposed to what we might estimate from our finite set of replicates."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### The sampling distribution as a function of sample size\n",
    "\n",
    "We can see what the estimated sampling distribution of the mean looks like at different sample sizes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "sample_means_at_size_10=sample_means[9]\n",
    "sample_means_at_size_100=sample_means[99]\n",
    "sample_means_at_size_1000=sample_means[999]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false,
    "figure_type": "m"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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02LlzZ2SzDRGlfV/0KJvNxnPPPRdtbW0jPNno0NHREd3d3bFv376CtWJ8bvbt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\nTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10ac524d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(sample_means_at_size_10, bins=np.arange(0,1,0.01), alpha=0.5);\n",
    "plt.hist(sample_means_at_size_100, bins=np.arange(0,1,0.01), alpha=0.4);\n",
    "plt.hist(sample_means_at_size_1000, bins=np.arange(0,1,0.01), alpha=0.3);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The distribution is much tighter at large sample sizes, and that you can have way low and way large means at small sample sizes. Indeed there are means as small as 0.1 at a sample size of 10, and as small as 0.3 at a sample size of 100. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Lets plot the distribution of the mean as a function of sample size."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false,
    "figure_type": "m"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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6OXdjUOuJk6bJDWS8/ghAWblvryQvskmLbQcAAKpqN51jIxVPuRyo35aeTPJT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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1091c0150>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for i in sample_sizes:\n",
    "    if i %50 ==0 and i < 1000:\n",
    "        plt.scatter([i]*200, sample_means[i], alpha=0.03);\n",
    "plt.xlim([0,1000])\n",
    "plt.ylim([0.25,0.75]);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### The kidney cancer case: higher variability at the extremes\n",
    "\n",
    "The diagram above has a tell-tale triangular shape with high and low means, and thus much larger variability at lower sample sizes.\n",
    "\n",
    "Consider the example of kidney cancers in various US counties from the lecture. Imagine that we have a statistical model or story for the occurence of kidney cancer. Let us think of each county as a sample in the population of kidney cancers, with the observations the per year occurence of cancer in that county. Then the low-population counties represent small size samples. The cancer rate in that county then is the sample mean of the cancer rates over multiple years in that county.\n",
    "\n",
    "Let us plot the incidence of kidney cancer against the size of the county:\n",
    "(diagram taken from http://faculty.cord.edu/andersod/MostDangerousEquation.pdf , a very worth reading aticle)\n",
    "\n",
    "![Age adjusted cancer rates are plotted against the log of the county population](cancergraph.png)\n",
    "\n",
    "We can see the entire pattern of low and high cancer rates in some parts of the country can entirely be explained from the smallness of the sample sizes: in a county of 1000 people, one cancer is a rate too high, for example. At the left end of the graph the cancer rate varies from 20 per 100,000 to 0. And the problem, as can be seen from the graph is onviously more acute at the upper end for the above reason. On the right side of the graph, there is very little variation, with all counties at about 5 cases per 100,000 of population.\n",
    "\n",
    "We'd obviously like to characterize mathematically the variability in the distribution of sample means as a function of the sample size.\n",
    "\n",
    "### The variation of the sample mean\n",
    "\n",
    "Let the underlying distribution from which we have drawn our samples have, additionally to a well defined mean $\\mu$, a well defined variance $\\sigma^2$. ^[The Cauchy distribution, as you know, is a well defined exception with ill defined mean and variance].\n",
    "\n",
    "Then, as before:\n",
    "\n",
    "$$V_{\\{R\\}}(N\\,\\bar{x}) = V_{\\{R\\}}(x_1 + x_2 + ... + x_N) = V_{\\{R\\}}(x_1) + V_{\\{R\\}}(x_2) + ... + V_{\\{R\\}}(x_N)$$\n",
    "\n",
    "Now in the limit of a very large number of replications, each of the variances in the right hand side can be replaced by the population variance using the law of large numbers! Thus:\n",
    "\n",
    "\\begin{eqnarray*}\n",
    "V_{\\{R\\}}(N\\,\\bar{x}) &=& N\\, \\sigma^2\\\\\n",
    "V(\\bar{x}) &=& \\frac{\\sigma^2}{N}\n",
    "\\end{eqnarray*}\n",
    "\n",
    "This simple formula is called **De-Moivre's** formula, and explains the tell-tale triangular plots we saw above, with lots of variation at low sample sizes turning into a tight distribution at large sample size(N).\n",
    "\n",
    "The square root of $V$, or the standard deviation of the sampling distribution of the mean (in other words, the distribution of sample means) is also called the **Standard Error**.\n",
    "\n",
    "We can obtain the standard deviation of the sampling distribution of the mean at different sample sizes and plot it against the sample size, to confirm the $1/\\sqrt(N)$ behaviour. \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "std_of_sample_means_1000 = [np.std(means) for means in sample_means_1000_replicates]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false,
    "figure_caption": "The slope of the graph is -0.5 showing the inverse proportion to the square root of N",
    "figure_type": "m"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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KbZFar52vJ80bueHhas/TI7sCsOS3g/xv1X4ADp64SOSSnUDho2KLYg6w92iK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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10ac84b90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(np.log10(sample_sizes), np.log10(std_of_sample_means_1000));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us plot again the distribution of sample means at a large sample size, $N=1000$. What distribution is this?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x10a8d3610>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(sample_means_at_size_1000, bins=np.arange(0.4,0.6,0.002));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Lets step back and try and think about what this all means. As an example, say I have a weight-watchers' study of 1000 people, whose average weight is 150 lbs with standard deviation of 30lbs. If I was to randomly choose many samples of 100 people each, the mean weights of those samples would cluster around 150lbs with a standard error of 30/$\\sqrt{100}$ = 3lbs. Now if i gave you a different sample of 100 people with an average weight of 170lbs, this weight would be more than 6 standard errors beyond the population mean, ^[this example is motivated by the crazy bus example in Charles Whelan's excellent Naked Statistics Book] and would thus be very unlikely to be from the weight watchers group."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### The Gaussian Distribution\n",
    "\n",
    "We saw in the last section that the sampling distribution of the mean itself has a mean $\\mu$ and variance $\\frac{\\sigma^2}{N}$. This distribution is called the **Gaussian** or **Normal Distribution**, and is probably the most important distribution in all of statistics.\n",
    "\n",
    "The probability density of the normal distribution is given as:\n",
    "\n",
    "$$ N(x, \\mu, \\sigma) = \\frac{1}{\\sigma\\sqrt{2\\pi}} e^{ -\\frac{(x-\\mu)^2}{2s^2} } .$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The expected value of the Gaussian distribution is $E[X]=\\mu$ and the variance is $Var[X]=s^2$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x10a23d890>"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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l5YwdO7Zf9zh//jwejweA7Oxszp492+05x48fZ9OmTdTU1PDAAw90e3z9+vWsWrWK6upq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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10b74df90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "norm =  sp.stats.norm\n",
    "x = np.linspace(-5,5, num=200)\n",
    "\n",
    "\n",
    "fig = plt.figure(figsize=(12,6))\n",
    "for mu, sigma, c in zip([0.5]*3, [0.2, 0.5, 0.8], colors):\n",
    "    plt.plot(x, norm.pdf(x, mu, sigma), lw=2, \n",
    "             c=c, label = r\"$\\mu = {0:.1f}, \\sigma={1:.1f}$\".format(mu, sigma))\n",
    "    plt.fill_between(x, norm.pdf(x, mu, sigma), color=c, alpha = .4)\n",
    "    \n",
    "    \n",
    "plt.xlim([-5,5])\n",
    "plt.legend(loc=0)\n",
    "plt.ylabel(\"PDF at $x$\")\n",
    "plt.xlabel(\"$x$\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### The Central Limit Theorem\n",
    "\n",
    "The reason for the distribution's importance is the Central Limit Theorem(CLT). The theorem is stated as thus, very similar to the law of large numbers:\n",
    "\n",
    "**Let $x_1,x_2,...,x_n$ be a sequence of independent, identically-distributed (IID) random variables from a random variable $X$. Suppose that $X$ has the finite mean $\\mu$ AND finite variance $\\sigma^2$. Then the average of the first n of them:**\n",
    "\n",
    "$$S_n = \\frac{1}{n} \\sum_{i=1}^{n} x_i ,$$\n",
    "\n",
    "**converges to a Gaussian Random Variable with mean $\\mu$ and variance $\\sigma^2/n$ as $n \\to \\infty$:**\n",
    "\n",
    "$$ S_n \\sim N(\\mu,\\frac{\\sigma^2}{n}) \\, as \\, n \\to \\infty. $$\n",
    "\n",
    "In other words:\n",
    "\n",
    "$$s^2 = \\frac{\\sigma^2}{N}.$$\n",
    "\n",
    "\n",
    "This is true, *regardless* of the shape of $X$, which could be binomial, poisson, or any other distribution."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Strictly speaking, under some conditions called Lyapunov conditions, the variables $x_i$ dont have to be identically distributed, as long as $\\mu$ is the mean of the means and $\\sigma^2$ is the sum of the individual variances. This has major consequences, for the importance of this theorem.\n",
    "\n",
    "Many random variables can be thought of as having come from the sum of a large number of small and independent effects. For example human height or weight can be thought of as the sum as a large number of genetic and environmental factors, which add to increase or decrease height or weight respectively. Or think of a measurement of a height. There are lots of ways things could go wrong: frayed tapes, stretched tapes, smudged marks, bad lining up of the eye, etc. These are all independent and have no systematic error in one direction or the other.\n",
    "\n",
    "Then the sum of these factors, as long as there are a large number of them, will be distributed as a gaussian.[\n",
    "At this point you are probably wondering: what does this have to do with the sampling distribution of the mean? We shall come to that, but in the meanwhile, lets consider some other key applications of the CLT.]\n",
    "\n",
    "As a rule of thumb, the CLT starts holding at $N \\sim 30$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "#### An application to elections: Binomial distribution in the large n, large k limit\n",
    "For example, consider the binomial distribution Binomial(n,k, p) in the limit of large n. The number of successes k in n trials can be ragarded as the sum of n IID Bernoulli variables with values 1 or 0. Obviously this is applicable to a large sequence of coin tosses, or to the binomial sampling issue that we encountered earlier in the case of the polling. \n",
    "\n",
    "Using the CLT we can replace the binomial distribution at large n by a gaussian where k is now a continuous variable, and whose mean is the mean of the binomial $np$ and whose variance is $np(1-p)$, since\n",
    "\n",
    "$$S_n \\sim N(p, \\frac{p(1-p)}{n}).$$\n",
    "\n",
    "The accuracy of this approximation depends on the variance. A large variance makes for a broad distribution spanning many discrete k, thus justifying the transition from a discrete to a continuous distribution.\n",
    "\n",
    "This approximation is used a lot in studying elections. For example, suppose I told you that I'd polled 1000 people in Ohio and found that 600 would vote Democratic, and 400 republican. Imagine that this 1000 is a \"sample\" drawn from the voting \"population\" of Ohio. Assume then that these are 1000 independent bernoulli trials with p=600/1000 = 0.6. Then we can say that, from the CLT, the mean of the sampling distribution of the mean of the bernoulli or equivalently the binomial is 0.6, with a variance of $0.6*0.4/1000 = 0.00024$. Thus the standard deviation is 0.015 for a mean of 0.6, or 1.5% on a mean of 60% voting Democratic.  This 1.5% if part of what pollsters quote as the margin of error of a candidates winning; they often include other factors such as errors in polling methodology.\n",
    "\n",
    "If one has results from multiple pollsters, one can treat them as independent samples from the voting population. Then the average from these samples will approach the average in the population, with the sample means distributed normally around it."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### What does this all mean?\n",
    "\n",
    "The sample mean, or mean of the random variables $x_{mi}$ in the sample $m$, has a sampling distribution with mean $\\mu$ and variance $\\frac{\\sigma^2}{N}$, as shown before. Now for large sample sizes we can go further and use the CLT theorem to say that this distribution is the normal distribution,\n",
    "\n",
    "$$S_N \\sim N(\\mu, \\frac{\\sigma^2}{N})$$.\n",
    "\n",
    "The preciseness of saying that we have a gaussian is a huge gain in our expository power. For example, for the case of the weight-watchers program above, a separation of 20lbs is more than 3 standard errors away, which corresponds to being way in the tail of a gaussian distribution. Because we can now quantify the area under the curve, we can say that 99.7\\% of the sample means lie within 9lbs of 150. Thus you can way easily reject the possibility that the new sample is from the weight-watchers program with 99.7\\% confidence. \n",
    "\n",
    "Indeed, the CLT allows us to take the reduction in variance we get from large samples, and make statements in different cases that are quite strong:\n",
    "\n",
    "1. if we know a lot about the population, and randomly sampled 100 points from it, the sample mean would be with 99.7\\% confidence within $0.3\\sigma$ of the population mean. And thus, if $\\sigma$ is small, the sample mean is quite representative of the population mean.\n",
    "2. The reverse: if we have a well sampled 100 data points, we could make strong statements about the population as a whole. This is indeed how election polling and other sampling works. (ADD MORE about what sample size is enough).\n",
    "3. we can infer, as we just did, if a sample is consistent with a population\n",
    "4. by the same token, you can compare two samples and infer if they are from the same population."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### The sampling distribution of the Variance\n",
    "\n",
    "At this point you might be curious about what the sampling distribution of the variance looks like, and what can we surpise from it about the variance of the entire sample. We can do this, just like we did for the means. We'll stick with a high number of replicates and plot the mean of the sample variances as well as the truish sampling distribution of the variances at a sample size of 100."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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Ra3AoLy+X1PnE4FKZmZmqqKiQYRiX3fgsXbr0svNs27ZNkjRy5Ei5XC7V1NQo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\nAD5UKzOUGgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10a66f1d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def make_throws_var(number_of_samples, sample_size):\n",
    "    start=np.zeros((number_of_samples, sample_size), dtype=int)\n",
    "    for i in range(number_of_samples):\n",
    "        start[i,:]=throw_a_coin(sample_size)\n",
    "    return np.var(start, axis=1)\n",
    "sample_vars_1000_replicates = [make_throws_var(number_of_samples=1000, sample_size=i) for i in sample_sizes]\n",
    "mean_of_sample_vars_1000 = [np.mean(vars) for vars in sample_vars_1000_replicates]\n",
    "plt.plot(sample_sizes, mean_of_sample_vars_1000);\n",
    "plt.xscale(\"log\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The \"mean sample variance\" asymptotes to the true variance of 0.25 by a sample size of 100. \n",
    "\n",
    "How well does the sample variance estimate the true variance? Notice that the histogram above ends at 0.25, rather than having ANY frequency at 0.25. What gives?\n",
    "\n",
    "If $V_m$ denotes the variance of a sample, \n",
    "\n",
    "$$ N\\,V_m = \\sum_{i=1}^{N} (x_{mi} - \\bar{x_m})^2 = \\sum_{i=1}^{N}(x_{mi} - \\mu)^2 - N\\,(\\bar{x_m} - \\mu)^2. $$\n",
    "\n",
    "Then\n",
    "$$E_{\\{R\\}}(N\\,V_m) = E_{\\{R\\}}(\\sum_{i=1}^{N}(x_{mi} - \\mu)^2) - E_{\\{R\\}}(N\\,(\\bar{x_m} - \\mu)^2)$$\n",
    "In the asymptotic limit of a very large number of replicates, we can then write\n",
    "$$E(N\\,V) = N\\,\\sigma^2 - \\sigma^2, $$\n",
    "and thus we have\n",
    "$$E(V) = \\frac{N-1}{N} \\,\\sigma^2$$.\n",
    "\n",
    "In other words, the expected value of the sample variance is LESS than the actual variance. This should not be surprising: consider for example a sample of size 1 from the population. There is zero variance! More genrally, whenever you sample a population, you tend to pick the more likely members of the population, and so the variance in the sample is less than the variance in the population.\n",
    "\n",
    "An interesting application of this idea, as Shalizi points out in http://www.stat.cmu.edu/~cshalizi/ADAfaEPoV/, is that the loss of variability due to sampling of genes is indeed the origin of genetic drift. More prosaically, the fact that the above graph of expected sample variance against sample size asymptotes to 0.25 is as $\\frac{N-1}{N}$ if very close to 1 at large N. \n",
    "\n",
    "Or put another way, you ought to correct your sample variances by a factor of $\\frac{n}{n-1}$ to estimate the population variance, which itself works as the sampling distribution of the sample variance is rather tight, as seen below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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BAAAAFAkGAACgSDAAAABFggEAACgSDAAAQJFgAAAAigQDAABQJBgAAIAiwQAA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\nAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10b7a3890>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(sample_vars_1000_replicates[99], bins=np.arange(0.2,0.26,0.001), alpha=0.2, normed=True);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### An application: Gallup Party Affiliation Poll\n",
    "\n",
    "Earlier we had used the Predictwise probabilities from Octover 12th to create a predictive model for the elections. This time we will try to **estimate** our own win probabilities to plug into our predictive model.\n",
    "\n",
    "We will start with a simple forecast model. We will try to predict the outcome of the election based the estimated proportion of people in each state who identify with one one political party or the other.\n",
    "\n",
    "Gallup measures the political leaning of each state, based on asking random people which party they identify or affiliate with. [Here's the data](http://www.gallup.com/poll/156437/heavily-democratic-states-concentrated-east.aspx#2) they collected from January-June of 2012:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Democrat</th>\n",
       "      <th>Republican</th>\n",
       "      <th>Dem_Adv</th>\n",
       "      <th>N</th>\n",
       "      <th>Unknown</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>State</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Alabama</th>\n",
       "      <td>36.0</td>\n",
       "      <td>49.6</td>\n",
       "      <td>-13.6</td>\n",
       "      <td>3197</td>\n",
       "      <td>14.4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Alaska</th>\n",
       "      <td>35.9</td>\n",
       "      <td>44.3</td>\n",
       "      <td>-8.4</td>\n",
       "      <td>402</td>\n",
       "      <td>19.8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Arizona</th>\n",
       "      <td>39.8</td>\n",
       "      <td>47.3</td>\n",
       "      <td>-7.5</td>\n",
       "      <td>4325</td>\n",
       "      <td>12.9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Arkansas</th>\n",
       "      <td>41.5</td>\n",
       "      <td>40.8</td>\n",
       "      <td>0.7</td>\n",
       "      <td>2071</td>\n",
       "      <td>17.7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>California</th>\n",
       "      <td>48.3</td>\n",
       "      <td>34.6</td>\n",
       "      <td>13.7</td>\n",
       "      <td>16197</td>\n",
       "      <td>17.1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            Democrat  Republican  Dem_Adv      N  Unknown\n",
       "State                                                    \n",
       "Alabama         36.0        49.6    -13.6   3197     14.4\n",
       "Alaska          35.9        44.3     -8.4    402     19.8\n",
       "Arizona         39.8        47.3     -7.5   4325     12.9\n",
       "Arkansas        41.5        40.8      0.7   2071     17.7\n",
       "California      48.3        34.6     13.7  16197     17.1"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gallup_2012=pd.read_csv(\"g12.csv\").set_index('State')\n",
    "gallup_2012[\"Unknown\"] = 100 - gallup_2012.Democrat - gallup_2012.Republican\n",
    "gallup_2012.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Each row lists a state, the percent of surveyed individuals who identify as Democrat/Republican, the percent whose identification is unknown or who haven't made an affiliation yet, the margin between Democrats and Republicans (`Dem_Adv`: the percentage identifying as Democrats minus the percentage identifying as Republicans), and the number `N` of people surveyed."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The most obvious source of error in the Gallup data is the finite sample size -- Gallup did not poll *everybody* in America, and thus the party affilitions are subject to sampling errors. How much uncertainty does this introduce? Lets estimate the sampling error using what we learnt in the last section"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Democrat</th>\n",
       "      <th>Republican</th>\n",
       "      <th>Dem_Adv</th>\n",
       "      <th>N</th>\n",
       "      <th>Unknown</th>\n",
       "      <th>SE_percentage</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>State</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Alabama</th>\n",
       "      <td>36.0</td>\n",
       "      <td>49.6</td>\n",
       "      <td>-13.6</td>\n",
       "      <td>3197</td>\n",
       "      <td>14.4</td>\n",
       "      <td>0.849059</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Alaska</th>\n",
       "      <td>35.9</td>\n",
       "      <td>44.3</td>\n",
       "      <td>-8.4</td>\n",
       "      <td>402</td>\n",
       "      <td>19.8</td>\n",
       "      <td>2.395543</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Arizona</th>\n",
       "      <td>39.8</td>\n",
       "      <td>47.3</td>\n",
       "      <td>-7.5</td>\n",
       "      <td>4325</td>\n",
       "      <td>12.9</td>\n",
       "      <td>0.744384</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Arkansas</th>\n",
       "      <td>41.5</td>\n",
       "      <td>40.8</td>\n",
       "      <td>0.7</td>\n",
       "      <td>2071</td>\n",
       "      <td>17.7</td>\n",
       "      <td>1.082971</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>California</th>\n",
       "      <td>48.3</td>\n",
       "      <td>34.6</td>\n",
       "      <td>13.7</td>\n",
       "      <td>16197</td>\n",
       "      <td>17.1</td>\n",
       "      <td>0.392658</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            Democrat  Republican  Dem_Adv      N  Unknown  SE_percentage\n",
       "State                                                                   \n",
       "Alabama         36.0        49.6    -13.6   3197     14.4       0.849059\n",
       "Alaska          35.9        44.3     -8.4    402     19.8       2.395543\n",
       "Arizona         39.8        47.3     -7.5   4325     12.9       0.744384\n",
       "Arkansas        41.5        40.8      0.7   2071     17.7       1.082971\n",
       "California      48.3        34.6     13.7  16197     17.1       0.392658"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gallup_2012[\"SE_percentage\"]=100.0*np.sqrt((gallup_2012.Democrat/100.)*((100. - gallup_2012.Democrat)/100.)/(gallup_2012.N -1))\n",
    "gallup_2012.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On their [webpage](http://www.gallup.com/poll/156437/heavily-democratic-states-concentrated-east.aspx#2) discussing these data, Gallup notes that the sampling error for the states is between 3 and 6%, with it being 3% for most states. This is more than what we find, so lets go with what Gallup says.\n",
    "\n",
    "We now use Gallup's estimate of 3% to build a Gallup model with some uncertainty. We will, using the CLT, assume that the sampling distribution of the Obama win percentage is a gaussian with mean the democrat percentage and standard error the sampling error of 3\\%. \n",
    "\n",
    "We'll build the model in the function `uncertain_gallup_model`, and return a forecast where the probability of an Obama victory is given by the probability that a sample from the `Dem_Adv` Gaussian is positive.\n",
    "\n",
    "To do this we simply need to find the area under the curve of a Gaussian that is on the positive side of the x-axis.\n",
    "The probability that a sample from a Gaussian with mean $\\mu$ and standard deviation $\\sigma$ exceeds a threhold $z$ can be found using the the Cumulative Distribution Function of a Gaussian:\n",
    "\n",
    "$$\n",
    "CDF(z) = \\frac1{2}\\left(1 + {\\mathrm erf}\\left(\\frac{z - \\mu}{\\sqrt{2 \\sigma^2}}\\right)\\right) \n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from scipy.special import erf\n",
    "def uncertain_gallup_model(gallup):\n",
    "    sigma = 3\n",
    "    prob =  .5 * (1 + erf(gallup.Dem_Adv / np.sqrt(2 * sigma**2)))\n",
    "    return pd.DataFrame(dict(Obama=prob), index=gallup.index)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "model = uncertain_gallup_model(gallup_2012)\n",
    "model = model.join(predictwise.Votes)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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Swvh8Pps/fz5jrKJ+DQ0N2ahRo6S2OXfuXMbn89mtW7cYY4xlZ2czPp/PhEIhe/HiBZdP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\nQuq9/wc1RWirfgw0FwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10adbe150>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "prediction = simulate_election(model, 10000)\n",
    "plot_simulation(prediction)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The predictive distribution is consistent with the real data -- the real outcome seems like a typical outcome according to the model. The accuracy is not very good as the center of the distribution falls fairly far from the observed outcome, but the precision is only marginally worse than in the predictwise case.\n",
    "\n",
    "But note that we used the Gallup voter self-identification from January to June to predict this, so we do not expect to do too well. And even though this is probably not a very unbiased sample, it still makes us wonder: at 97\\% of simulations showing a win for Obama, why did Romney ever think he had a chance?"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}
